Effects of time delays in replicator dynamics were discussed in [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}
for games with an interior stable equilibrium (an evolutionarily stable strategy [13]}, [14]}).
In [1]}, the authors discussed the model, where individuals at time \(t\)  imitate a strategy with a higher average payoff
at time \(t-\tau \)  for some time delay \(\tau \) . They showed that the interior stationary state of the resulting time-delayed differential equation
is locally asymptotically stable for small time delays and for big ones it becomes unstable, there appear oscillations.
In [2]}, we constructed a different type of a model, where individuals are born \(\tau \)  units of time after their parents played.
Such a model leads to system of equations for the frequency of the first strategy and the size of the population.
We showed the absence of oscillations – the original stationary point is globally asymptotically stable for any time delay.
In both models, the position of the equilibrium is not affected by time delays.
